the relevance of ocean surface current in the ecmwf

The relevance of ocean surface current in the ECMWF analysis andforecast system

Hans Hersbach and Jean-Raymond Bidlot

ECMWF, Shinfield Park, ReadingRG2 9AX, United [email protected]

ABSTRACT

This document describes a preliminary adaptation of the integrated forecast system at ECMWF to incorporate ocean sur-face currents from an external source. An impact study is performed in a data-assimilation environment, which allows forboth a proper adjustment of the atmospheric boundary condition and a suitable adaptation of the ingestion of observationsthat are sensitive to the ocean surface. It is found that the effect on surface stress is only about half of what would havebeen intuitively obtained by subtraction of the ocean current from the surface wind of a system in which no account forocean current is given. As a result, compared to the intuitive approach, the effect on wind-generated ocean waves is foundto be reduced.

1 Introduction

The European Centre for Medium-Range Weather Forecasts (ECMWF) has a coupled ocean-atmosphere sys-tem for seasonal and monthly forecasting (Vitart et al., 2008). The seasonal system is fully coupled. Themonthly forecasts are at present only coupled from day 10 onwards (which runs at a lower resolution). More-over, in contrast to the seasonal system, that coupling doesnot include ocean currents.

At first sight, the importance of ocean currents seems minor.The strength of typical ocean currents is in theorder of a few tenths of ms−1, which is small compared to typical surface wind speed of around 8 ms−1.Nevertheless, in tropical areas the ratio between the two can be 1 ms−1 versus 5 ms−1. For ocean-wave fore-casting there may be a noticeable effect. Tropical ocean currents can deflect swell, which affect the propagationover the length scale of an ocean basin of 10,000km. Wave-current interactions in western boundary currents,such as the Gulf Stream, are well known.

At ECMWF, work has recently started to include the effect of ocean current on the ECMWF atmosphere andocean-wave model component for the medium range. Although the technical development in the ECMWFintegrated forecast system (IFS) has in principle been completed, it should be stressed that at this stage noproper assessment has been made. The results described in this presentation should therefore be interpreted aspreliminary. The focus will be on ocean waves and surface wind.

In Section2, it is described how the boundary condition of an atmospheric model is adapted to include oceansurface current. Some simple considerations are presentedon how an ocean current is expected to change the airflow near the surface. Section3 handles the incorporation of ocean current in the ECMWF ocean-wave modelWAM. Results of a few hindcast runs are presented in Section4. Section5 deals with necessary changes in theassimilation component of the ECMWF model. In section6 an impact study of the coupled wave-atmospheresystem is described. The document ends with a discussion in Section7.

ECMWF Workshop on Ocean-atmosphere interactions, 10-12 November 2008 61

HERSBACH AND BIDLOT: ASSESSMENT OF OCEAN CURRENT ATECMWF

2 Inclusion of ocean current in the atmospheric boundary layer

In principle the inclusion of an ocean surface current in theatmospheric component is straightforward. Letthe flow with respect to a coordinate frame that is fixed with respect to the Earth be denoted by~uabs. This isthe usual frame in which numerical weather models, including ECMWF, are defined. All what is required toinclude surface current is that the no-slip condition at thesurface demands that the (absolute) flow at heightz= 0 equals the ocean current~uoc, rather than being zero:

~uabs(z= 0) =~uoc. (1)

In the ECMWF operational integrated forecast system (IFS),the lowest model level (out of 91 levels) is de-signed to be close to a height of 10m. It is assumed that between this layer and the surface the constant(turbulent) stress assumption is valid, using a form of Monin-Obukhov stability theory. For a certain valueof stress~τ = ρau∗~u∗, whereρa is the air density,~u∗ the friction velocity andu∗ its magnitude, the followingvertical equation, together with boundary condition (1) is to be satisfied:

∂~uabs

∂z=

~u∗

κ(z+z0)ΦM

(

z+z0

L

)

. (2)

Hereκ = 0.4 is the von Karman constant,ΦM is a stability-dependent gradient function andL is the Obukhovlength. Detailed definitions on these quantities may be found in Part IV.3 of theIFS-documentation(2006). Theroughness lengthz0 depends for light wind on the kinematic viscosityν (1.5x10−5 m2s−1) and on a Charnockrelation for strong wind as:

z0 = αMνu∗

+ αchu2∗

g. (3)

HereαM = 0.11, g = 9.81 ms−2 is the gravitational acceleration, andαch depends on the sea state, and is onaverage 0.018. Typical values forz0 are within the range from 0.01 mm to 1 mm, i.e., the sea surfaceis verysmooth. Integration of (1-3) in the ECMWF model, which includes the determination of thevalue of stress,depends on the details of the flow higher up in the atmosphere.

Given a solution for~uabs, define~urel as the flow relative to a frame moving with the ocean current:

~uabs(z) =~urel(z)+~uoc. (4)

This relative flow then also satisfies (2), but with the more familiar boundary condition:

~urel(0) = 0. (5)

The formal solution of (2, 5) is given by:

~urel(z) =~u∗

κ

ln

(

z+z0

z0

)

−ΨM(z+z0

L)+ ΨM(

z0

L)

, (6)

whereΦM(η) = 1−ηΨ′M(η). Therefore, it is the relative flow, rather than the absoluteflow that is connected

to the surface stress. Also, the surface dragCD connects the stress with~urel(10 m), rather than~uabs(10 m):

τ/ρa = CD~u2rel(10 m). (7)

Among other quantities, it is the stress that provides the communication of the atmosphere with other compo-nents. This is for instance the case for the growth of ocean (surface) waves.

The question arises how the presence of an ocean current willaffect the flow. The answer depends on therelative importance between the boundary conditions at thesurface and higher up in the atmosphere. Let thewind profile in the absence of ocean currents be given by~unocur. In this case~unocur is equal to both the absoluteand relative flow. In Figure1 an example of a wind profile in a neutral boundary layer with a friction velocity

62 ECMWF Workshop on Ocean-atmosphere interactions, 10-12November 2008


Figure 1: Logarithmic wind profiles near the ocean surface inan absolute frame. The blue dotted profile isfor u∗ = 0.3 ms−1 without ocean current. The green dash-dotted profile represents the situation of an oceancurrent of1 ms−1 aligned with the wind direction and where the stress has beenfixed, and the red dashedprofile for a similar situation, but where the wind speed at a height of100 mhas been fixed.

of 0.3 ms−1 is presented by a blue dotted line. In this caseΨM = 0, so (6) follows the well-known logarithmicprofile. This choice corresponds toz0 = 0.17 mm andunocur(10 m) = 8.24 ms−1.

Assuming that the boundary condition at the surface would dominate conditions higher up in the atmospherewould imply that the surface stress remains unchanged. Since stress is related to the relative wind, profile (6)would not be altered. The entire absolute wind profile (including higher up in the atmosphere) would be shifted:

~uabs(z) ∼~unocur(z)+~uoc, ~urel(z) ∼~unocur(z). (8)

This is in principle a viable solution, since~urel satisfies (2, 3, 5). Only the boundary condition higher up isto be shifted by~uoc. In Figure1~uabs is displayed by the green dot-dashed curve for the situationthat thereis an ocean current of 1 ms−1 in the direction of surface wind. Roughness length and friction velocity areunchanged,uabs(10 m) is enhanced by 1 ms−1 to 9.24 ms−1.

A more plausible assumption is that the boundary in the free atmosphere would be dominant. This favours themaintenance of the absolute wind profile, and it is the relative profile that is now shifted:

~uabs(z) ∼~unocur(z), ~urel(z) ∼~unocur(z)−~uoc. (9)

Since~urel has changed, and thus according to (6) the stress, this solution does not exactly satisfy (2, 3, 5),and the entire profile has to be reintegrated. For the examplepresented in Figure1, assume that the boundarycondition is unaltered at a height of 100 m. When, for the sakeof simplicity it is assumed that the constant stressapproximation could still be used at this height, reintegration of (1-3), together with conditionuabs(100 m) =unocur(100 m), leads to the red dashed profile. As a result, surface stress and roughness length are somewhatreduced (u∗ from 0.30 ms−1 to 0.27 ms−1, andz0 from 0.17 mm to 0.14 mm). The absolute wind speed hasincreased from 8.24 ms−1 to 8.44 ms−1, rather than to remain unchanged as (9) suggested. In this case, itappears that the stress goes down while the (absolute) wind speed goes up. This can be explained simply by thepicture that the movement of the surface in the direction of the flow decreases the friction (stress) at the surface,which therefore slows down the flow near the surface to a lesser extent. The change in relative wind speed is0.80 ms−1, rather than what was expected by (9) (1.00 ms−1).

In practice both the boundary conditions at the surface and higher up in the atmosphere will play a role. Theexample of Figure1 may be over simplistic, but it does illustrate that a moving ocean current will affect



surface stress, and therefore the entire wind profile. At 10-metre height, absolute wind speed is expected toincrease somewhat for an ocean current in the direction of the flow (‘less friction‘), and to decrease somewhatwhen the current is opposite to the flow (‘more friction‘). Asa result, assumption (9) will not be completelycorrect. Therefore the effect of ocean current on surface stress cannot be immediately guessed from operationalECMWF 10-metre wind in which no information on ocean currenthad been supplied to the boundary condition.Although in lowest approximation the assumption that absolute wind at 10-m height is unaffected by an oceancurrent may be reasonable, some fractionx of ~uoc will be absorbed in~uabs(10 m), leaving a fraction 1− x fora change in relative wind, and thus the surface stress. Therefore, the effect of ocean current on surface stressmay be smaller than one may expect at first sight. The simple example given above suggests a reduction in theorder of 20%. Of course, only a proper integration of the model with inclusion of (1) can provide quantitativeestimates.

3 The inclusion of ocean current in ocean wave forecasting

At ECMWF, ocean-surface wave forecasting is an integral part of the IFS. This is achieved by two-way couplingof the atmosphere model with a wave model (Janssen, 2004). The ocean-wave model is a derivative fromWAM (Komenet al., 1994), which is a third-generation model that provides an evolution of the wave spectrumF(~k,~x, t) . This quantity represents the energy density of ocean waveswith wave vector~k within an area aroundposition~x that is sufficiently large compared to the length of the wavesthemselves. The basic transport equationis given by:

∂∂ t

+(~cg +~uoc) ·∂

∂~x− (

∂∂~x

Ω) ·∂

∂~k

(

Fσ

)

= Sin +Snl +Sds+Sbot. (10)

Here

σ(~k,~x) =

√

g||~k|| tanh(||~k||d(~x)), ~cg =∂

∂~kσ and Ω(~k,~x, t) = σ +~k ·~uoc (11)

are respectively the intrinsic frequency, group velocity and dispersion relation.d is the local water depth. Thisequation expresses that any change in wave action(F/σ) is imposed by (in space) local sources and sinks,which are wave growth due to wind inputSin, non-linear interaction between wavesSnl, and dissipation dueto white-cappingSds and bottom frictionSbot. At ECMWF, an equation forF rather thanF/σ is solved byan appropriate rewriting of (10). Details on the physical description and numerical implementation of theoperational WAM model at ECMWF may be found in Part VII of theIFS-documentation(2006).

The wind inputSin, which is based on a formulation ofJanssen(1991), describes the interface with the atmo-sphere. Wave growth due to wind mainly depends on the ratio between the component of friction velocity~u∗ inwave propagation direction and phase speed, and some additional quantities such as air density and atmosphericstability. These quantities are provided by the atmospheric component. For historical reasons, the neutral windat 10-metre height, rather than the friction velocity is passed to the wave model:

~un =~u∗

κln(

10+z0

z0). (12)

According toJanssen(1991), the ocean-wave spectrum influences the Charnock parameter αch. This wave-agedependent quantity is passed back to the atmosphere, where it is used in (3) to update the sea-surface roughnesslength.

Regarding ocean currents, there are two contributions. First of all, the effect of the current on the wind profile,as described in the previous section, will affect the stress, and thus the neutral wind (12). This change shouldin principle be incorporated in the atmospheric component of the IFS.

The other contribution regards the advection term in the lhsof (10) and dispersion relationΩ in (11). Dueto a horizontally inhomogeneous ocean current field, wave refraction may occur, swell will deflect, and oceanwaves can even be blocked or reflected. This intrinsic effecton ocean waves is in principle incorporated in the



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standard formulation of the wave model. It should be noted that in the derivation of (10) it has been assumedthat the ocean current does not depend on depth in the few tensof metres near the surface where they couldinfluence the ocean waves.

4 An ocean-wave hindcast study

In this section some potential impact of ocean current on ocean-waves will be explored in a hindcast environ-ment. In such a set-up, the wave model is forced by given ECMWFanalysis fields. Any feedback from thewaves on the atmosphere (viaαch) is disregarded. Another simplification is that the detailed effect of oceancurrent on the atmosphere is not taken into consideration. It is assumed that the model absolute wind~uabs isunaltered, and that the entire effect of the ocean current isabsorbed in the relative current~urel. Therefore aseparate set of atmospheric analyses fields does not have to be provided to incorporate the effect of ocean cur-rent on the wind forcing. Relation (9) applied to the neutral wind~un can be followed, instead. Although theseassumptions may not appear to be perfectly justified, they doprovide a simple but effective way to investigatethe direct impact of ocean currents on ocean waves.

The question on the source for ocean current now arises. Requirements are a sufficient resolution on a globalscale and a proper assimilation system, such that realisticfeatures are resolved and well described. Exampleswould include a sharp definition of the Gulf stream, equatorial currents and counter-currents, and eddies. For thereason of consistency it is desirable that the ocean model from which the currents will originate has been forcedwith ECMWF (analysis) fluxes. Several candidates have been considered. One example is the TOPAZ3 systemfrom NERSC (TOPAZ, 2007). It is based on the modified HYCOM ocean model with a resolution between8-12 km. Its data assimilation embodies an Ensemble Kalman Filter using 100 members. Atmospheric forcingis from ECMWF. This model is only run in the Atlantic area. Although this system, therefore, is not suitablefor conducting a global impact study, some experimentationhas been performed for the high-resolution limited



area wave model that is run operationally at ECMWF for the North-Atlantic and Mediterranean. Results ofthese experiments, though, will not be reported in this document.

Another good candidate is the ocean model fromMERCATOR(2007). This system involves the NEMO oceanmodel and is run on a horizontal resolution of 0.25 degrees on a global scale (disseminated products are onlyavailable at 0.5 degree). Daily analysis fields are available and are based on a Kalman-Seek method. Itsatmospheric forcing also arises from ECMWF. The impact studies presented in this document will be based onthis system. An example of a MERCATOR ocean surface current field is displayed in Figure2. It shows a verywell defined Gulf stream and Loop current.

Several hindcast experiments were conducted for the periodbetween 17 March and 20 April 2008. All ex-periments involved the same setup of the global wave model, which was run at a slightly reduced horizontalresolution than the present operational resolution (0.5 degrees, rather than 0.36 degrees). The number of wavedirections (24) and frequencies (30) was equal to the operational configuration.

A control experiment (to be called HCNTRL) involved a run without any current effects. A second experiment(denoted by HCWIND), only took the effect of the current on the wind input into account. This was, asdiscussed above, handled by the choice:

~un(HCWIND) =~un(HCNTRL)−~uoc(MERCATOR). (13)

A third experiment (named HCWADV) concentrated on the effect of currents on the wave advection. Theforcing wind field was not adapted for this run, so~un(HCWADV) =~un(HCNTRL). A fourth experiment,including both the effect on wind forcing and wave advectionwas conducted as well. Since its results appearedmore or a less the sum of the results from the HCWIND and HCWADVruns, this experiment will not be furtherdiscussed.

Some average results are summarized in Figure3. Top panel shows the average difference in wind speed ofapplied wind forcing for the HCWIND experiment. Locally differences can exceed 0.5 ms−1. On average,ocean currents are in the direction of the prevalent wind regime, so the relative wind speed has reduced. Thisis for instance the case along the Antarctic Circumpolar (ACC) Current and the North and South Equatorialcurrents. As a result, wave height has reduced in most areas around the globe, especially along the ACC. In thetropics, the Equatorial Counter Current enhances the relative wind speed. Here, wave height is increased. Noclear effect from the Gulf stream on wind speed emerges from the top panel of Figure3. The reason for thisis that the Gulf Stream current and the typical westerly winds are not aligned. When a vector difference wouldhave been plotted a clear difference would have emerged. Theeffect on wave height in the region in the NorthAtlantic is a slight decrease in wave height. On average the response of wave height is modest. In isolatedextreme cases, though, the effect may be up to 1 m. So althoughthe average wave climate does not change toomuch, from the point of view of case by case ocean-wave forecasting there may be a significant effect.

The lower panel of Figure3 shows the average response of wave height on the advection. The patterns for thisHCWADV experiment are more large scale than the effect from the HCWIND run. It indicates that typicallyswell is affected, which acts on a long spatial scale. There are some more intense responses in the tropics, whichare related to sharp gradients in the ocean current. The areaEast of the Philippines, for instance, indicates aresponse to the New Guinea Coastal Current.

5 The inclusion of ocean current in the ECMWF 4D-Var assimilation system

The provision of the boundary condition (1) has been prepared in the ECMWF forecast model some time agoby Anton Beljaars. It would be straightforward to see the effect in a model integration. Starting from someinitial condition and enforcing some ocean current field, like the MERCATOR field as used in the previoussection, the difference with a standard control run that didnot include currents can reveal the impact of suchchange. The initial condition for the model forecast arisesfrom a data assimilation suite, where knowledge



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from a previous forecast (also called the first guess or background) is mixed with new observational data. Suchassimilation steps are essential, since without them, the forecast will soon loose any connection with reality.Since both the experiment and control would start from the same analysis, it takes some time for the effect ofocean currents to become visible. It would be better and moreconsistent to include the effect of ocean currentsin the assimilation system as well. In this way the information of the ocean current will be able to cycle throughthe system. The impact is then to be assessed by the comparison of two assimilation suites, one with and onewithout ocean current. Many systems that use the ECMWF modelas boundary condition are based on analysisfields, rather than forecast fields. An example are ocean models themselves. Both MERCATOR and TOPAZ,for instance, use ECMWF fluxes to drive their ocean models. Also from this point of view it is desirable toproperly adapt the assimilation system, since ocean-current information that flows in from the model first-guesscan be wiped out by surface observations when the effect of ocean current is neglected in the assimilation. Theadaptation of the assimilation system would be a requirement when the usage of ocean currents is to become apart of the operational assimilation and forecast system atECMWF.

ECMWF uses the method of incremental four-dimensional dataassimilation (denoted by 4D-Var,Courtieret al.(1994)). For a given assimilation window, data is collected and compared to the model state via a cost functionJ that is to be minimized with respect to an incrementδx that corrects the backgroundxb at the start of theassimilation window. Schematically,J is given by:

J(δx) = Jb +Jo =12

δxTB−1δx+12(Hδx−d)TR−1(Hδx−d). (14)

As stated above, the background is a short forecast from the previous analysis cycle. TheJb term expresses theconfidence in this field via the background error covariance matrix B. At the end of the minimization, the finalincrementδxa is added to the backgroundxb to provide the analysisxa = xb + δxa.

The comparison between model and data is obtained via an observation operatorH. It expresses what the valueof observation should be according to the model. In 4D-Var the comparison between model and observationincorporates the timing of the observation as well. As a function of initial model state,H therefore includes amodel integration from initial time to observation time. In(14), H is a suitable linearization ofH around thebackground, while the covariance matrix of observation errors R expresses the accuracy of the observationalnetwork. The innovation vectord is given by:

d = yo−H(xb), (15)

where the set of observations within the assimilation window is represented as a vectoryo. The model integra-tion started from the background over the entire assimilation window, that is required to calculateH for eachobservation in (15), is called the trajectory run (or outer loop). It is performed at the same resolution as theforecast model. Minimization (14), though, is performed at a reduced resolution (inner loop). This means thatincrementsδx and linearizationH are performed at a lower resolution, while innovationd is calculated at fullmodel resolution. The sequence of outer and inner loop is iterated a few times, in which the high resolutiontrajectory is readily updated. For the following discussion, though, the complication of inner and outer loops isnot essential and its technical implications will not be further mentioned. A detailed description may be foundin Part II of theIFS-documentation(2006).

The contribution of ocean current to the assimilation system is basically concentrated in the observation oper-atorH. First of all, the trajectory run that involves the plain integration of model fields on model levels fromthe background over the assimilation window should satisfyboundary condition (1). This is straightforward,since that part is already available. Secondly, for observations that measure quantities near the sea surface theobservation operator may have to be adapted. Such changes have to be handled separately, since the physicspackage that is used inH to calculate surface quantities from model variables at model levels, is not sharedwith the physics in the forecast model (Cardinaliet al., 1994). For instance, the wind at an observation heightz near or below the lowest model levelzL is estimated on the basis of a method byGeleyn(1988). Given theconstant stress approximation no wind turning takes place and the wind vector is given by a simple reductionR from the wind vector at the lowest model level. Geleyn proposes the use of simplified gradient functionsΦM



in (2) which then allows for the estimation of the value ofR from available model quantities at lowest modellevel plus a knowledge of roughness lengthz0. Since the method of Geleyn is based on a non-moving surface,it should now be applied to relative wind:

~urel(zobs) = R~urel(zL) = R(~uL −~uoc), (16)

where it is realized that the model wind~uL at lowest model level is defined in the absolute frame.

Let for a surface vector wind observation~uobs, the observation operatorH be denoted by~umod. Then the partof Jo in (14) that belongs to that specific observation is given by

Jsurfwindo =

||~umod−~uobs||2

σ20

, (17)

whereσ0 determines the observation weight. It now depends on the nature of the surface wind observationhow~umod is to be adapted. One source of wind observations that is usedextensively at ECMWF is fromscatterometer data (Isaksen and Janssen(2004), Hersbach and Janssen(2007)). A scatterometer is a microwaveradar that emits pulses at well-defined frequency and polarization to the ocean surface. The magnitude ofrecorded backscatter is a measure for the strength of gravity-capillary surface waves. Since these waves respondto the local surface stress on a short time scale, they can be regarded as fully grown wind waves. Therefore, it isreasonable to suggest a one-to-one relation between backscatter and stress. Although different scatterometersmay sense the surface at different frequencies (e.g., C-band or Ku-band), a unique relation between backscatterand stress should exist for each of them. For practical reasons, backscatter is usually related to 10-metre(neutral) wind, on the basis of an empirical geophysical model function. Examples are the QSCAT-1 modelfunction for Ku-band (QuikSCAT, NSCAT, for an overview seeChelton and Freilich(2005)), and CMOD5(Hersbachet al., 2007) for C-band (ERS and ASCAT). Observational evidence that scatterometer measure windrelative to a moving ocean surface was found byKelly et al. (2001).

Another source of surface wind observations is from buoy andship data. Moored buoys, such as the TAO arrayevidently measure wind with respect to an absolute frame. Insummary, the adaptation of observation operator~umod depends on the nature of the observation as:

scatterometer : ~umod =~urel(z10) = R(~uL −~uoc), (18)

buoy/ship : ~umod =~uabs(zobs) = R~uL +(1−R)~uoc. (19)

In the absence of ocean currents, (18) and (19) reduce to the observation operators for the operational assimila-tion system, i.e.,~umod= R~uabs(zL). The observation operator for scatterometer data should strictly speaking acton equivalent neutral wind (12), or even better on~u∗ (to account for sea-state effects inz0), rather than relativewind. Although the modification for neutral wind has been prepared (by a suitable redefinition ofR), this willnot be discussed here. The lowest model level is in practice very close to 10 m, soR≈ 1 in (18).

For buoy observations, adaptation (19) tries to hold on absolute wind. Many buoys measure wind at a height of 4or 5 m, soR< 1. Relation (19) then illustrates that ocean currents can have an effect on an observation operatorfor wind measured in a fixed frame. In case model wind and oceancurrent are not aligned the observationoperator will involve a change in wind direction. In practice though, the effect will be small. For the examplegiven in Figure1, e.g.,R= 0.92 so nearly unity.

6 A data assimilation impact study

This section will present some results of an impact study within a data assimilation environment. In contrastto the hindcast study as discussed in Section4, the ECMWF analysis winds that force the ocean-wave modelare now subject to changes induced by the ocean currents, rather than being prescribed. In the final 4D-Vartrajectory, wave data (such as altimeter wave height and SARwave spectra) are assimilated and waves and



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Figure 4: Difference in neutral wind speed (top panel, inms−1), 10-metre absolute wind (middle panel,in ms−1) and significant wave height (lower panel, inm) between the DAWIND and DACNTR experimentaveraged over the period 17 March to 20 April 2008.



atmosphere are two-way coupled. In an assimilation experiment information that is ingested in one cycle ispropagated forward into the next cycle. It may be clear that this setup provides a more consistent frame work.

The adaptation of the assimilation system as described in the previous section was prepared. The observa-tion operator (18, 19) was adapted. Regarding linearization (i.e.H in minimization14), associated tangent-linear and adjoint code was updated. An infrastructure for the inclusion of an ocean current from an externalsource was developed in a way that is similar to the ingestionof sea-surface temperature and sea-ice fraction atECMWF. Since boundary condition (1) is respected in both the trajectory of 4D-Var and in the short-forecastrun that connects subsequent analysis cycles, the full effect of ocean current is incorporated in the neutral wind(12). It is, therefore to be passed on directly to the ocean-wavemodel without any further corrections.

Two data assimilation experiments were conducted, a control (DACNTR) without, and an experiment (DAWIND)with the inclusion of ocean currents. In the latter experiment only the effect on the wind forcing (via the neu-tral wind from the adapted atmosphere) was taken into account. For technical reasons (that have meanwhilebeen resolved) it was not possible at the time to conduct a third experiment that includes the effect on waveadvection.

The data assimilation experiments were performed for the same period as the hindcast study of Section4 (17March to 20 April 2008). For the DAWIND experiment, the same ocean current fields fromMERCATOR(2007) were used. The resolution of the wave model was again 55 km inthe horizontal, and 24 directionstimes 30 frequencies in wave-vector space. The horizontal resolution of the atmospheric model was reducedcompared to the ECMWF operational system, i.e., T511, rather than T799 in spectral space, which correspondsto 40 km versus 25 km. The number of vertical levels was the same (91). The assimilation window was,like the operational suite, 12 hours, although experimentswere not run in early-delivery mode (see ChapterII, IFS-documentation(2006)). For each day, a 10-day forecast was started from the analysis centred around00UTC. The impact on these forecasts will not be discussed here, though.

The top panel of Figure4 displays the average change in neutral wind speed (12) at analysis time. The effectappears to be significantly smaller than what was assumed in the hindcast study (top panel of Figure3). Onlyabout half of the effect of the ocean current is absorbed by the relative wind~urel (6), which, apart from stabilityeffects is closely related to the neutral wind (12). The remaining 50% is shifted into a change in the absolutewind. This is shown by the middle panel of Figure4. Where ocean current and wind are aligned, absolute windin general increases (like displayed in Figure1), where ocean current and wind are opposed absolute windspeed decreases. This seems especially to be an issue in the tropics. Hence, it appears that the assumption (9)that absolute wind can be regarded as nearly unaffected, on which the hindcast runs were based, is not justified.In line with a reduced effect on wind forcing, the response ofthe ocean-wave model is smaller as well. Thelower panel of Figure4 shows the impact in significant wave height for the DAWIND experiment, which isindeed much smaller than the impact in the HCWIND hindcast (middle panel of Figure3).

7 Discussion

The reduced impact on the relative and neutral wind, due to the response of the absolute wind to an appliedocean current can originate from several effects. A first argument is along the lines of the simple examplepresented in Section2 and Figure1. It was shown there, that strictly speaking assumption (9) does not providea valid solution. Due to a lower (enhanced) stress in case ocean current is aligned with (opposed to) the surfacewind, the friction of the boundary layer with the ocean surface is enhanced (reduced) which, given more orless unaltered geostrophic conditions in the free atmosphere, will result in higher (lower) surface wind. For theexample of Figure1, where the original blue profile was slightly shifted (red profile), the effect was guessedto be 20%. Boundary condition (1) acts in both the 4D-Var trajectory and the short forecasts in betweenassimilation cycles. Therefore this effect is present in both the assimilation and forecast.

A second factor behind the reduced effect on relative wind may originate from the adapted assimilation system.



Since scatterometer data now act on relative model wind, theassimilation system will try to hold on the samevalues for stress at observed locations for the DAWIND and DACNTR experiment. For the example in Figure1,the assimilation system would favour the situation of shifting the original blue profile (DACNTR) to the greencurve (DAWIND), i.e., for a 100% shift of the ocean current into the absolute wind. Although at ECMWFscatterometer data is ingested in most areas within a 6-hourtime window, the adapted observation operatorwill compete with other observations in which no adaptations were required. Among other reasons, this willlimit the effect from scatterometer data. At first thought, it might be contradictory that the proper treatment ofscatterometer data limits the impact. One should, however,realize, that the reason for this is not related to theexperiment that includes ocean current (DAWIND), but due toan incorrect assimilation of scatterometer dataas absolute wind in the DACNTR experiment. For this reason, to a limited extent, operational ECMWF surfacewind may represent wind in a relative frame rather than in an absolute frame.

As mentioned, the work presented in this document is preliminary. Sofar, only a first assessment is being madein the basic understanding of the effect of an ocean current on the ECMWF assimilation and forecast system. Inthe next step, impact on forecast skill is to be taken seriously. The issue could be raised to what level of accuracyocean currents are to be, and can be provided. A comparison betweenMERCATOR(2007) andTOPAZ(2007)showed that although both ocean models contain similar mainstructures (tropical currents and counter-currents,Gulf Stream, Kuroshio Extension, etc.), differences in theresolved Eddies are noted. Possibly some averagingmay have to be performed to filter out uncertain features. Also, it may be queried to what level it is justifiedto keep the supplied currents constant during a 10-day integration. For extreme and rapidly moving systems,such as tropical cyclones, a response of the ocean current onan evolving atmosphere, may require a two-waycoupled ocean-atmosphere system from the start of the forecast.

Acknowledgements

We would like to thank Anton Beljaars, Peter Janssen, Tim Stockdale, Magdalena Alonso Balmaseda andFrederic Vitart for their useful discussions and suggestions. The work presented in this document was partlyfunded by ESRIN (Project Ref. 22025/08/I-EC). We would liketo thank MERCATOR OCEAN for the kindprovision of their ocean-current data.

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the relevance of ocean surface current in the ecmwf

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